Surveys in Mathematics and its Applications
Volume 1 (2006), 41 - 49
OPTIMAL ALTERNATIVE TO THE AKIMA'S METHOD OF SMOOTH INTERPOLATION APPLIED IN DIABETOLOGY
Alexandru Mihai Bica, Marian Degeratu, Luiza Demian and Emanuel Paul
Abstract. It is presented a new method of cubic piecewise smooth interpolation applied to experimental data obtained by glycemic profile for diabetics. This method is applied to create a soft useful in clinical diabetology. The method give an alternative to the Akima's procedure of the derivatives computation on the knots from  and have an optimal property.2000 Mathematics Subject Classification: 57R12, 65D05.
Keywords: piecewise smooth interpolation, smooth approximations, quadratic oscillation in average, least squares method.
- H. Akima, A new method for interpolation and smooth curve fitting based on local procedure, J. Assoc. Comput. Mach. 17 (1970), 589-602. Zbl 0209.46805.
- A. M. Bica, Mathematical models in biology governed by differential equations, PhD Thesis Babeş-Bolyai University Cluj-Napoca 2004.
- A. Bica, Lyapunov function for a bidimensional system model in the blood glucose homeostasis and clinical interpretation, Int. J. Evol. Equ. 1, no. 1 (2005), 69--79. MR2144218(2005m:92010). Zbl 1094.34029.
- A. M. Bica, M. Curilă and S. Curilă, Optimal piecewise smooth interpolation of experimental data, Proceedings of ICCCC2006 (International Conference on Computing, Comunications, Control, 2006), Oradea, 74-79.
- C. Iacob(ed), Classical and modern mathematics}, vol.4, Ed. Tehnica, Bucharest 1983 (in Romanian).
- K.Ichida, F.Yoshimoto and T. Kiyono, Curve fitting by a Piecewise Cubic Polynomial, Computing 16 no. 4 (1976), 329--338. MR0403168(53 #6981). Zbl 0321.65010.
Acknowledgement. The research of the first author on this paper is supported by the grant 2Cex-06-11-96 of the Romanian Government.
Alexandru Mihai Bica Marian Degeratu University of Oradea, University of Oradea, Department of Mathematics and Informatics, Department of Mathematics and Informatics, Str. Universitatii no.1, 410087, Oradea, Str. Universitatii no.1, 410087, Oradea, Romania. Romania. email@example.com, firstname.lastname@example.org email@example.com Luiza Demian Emanuel Paul University of Oradea, University of Oradea, Faculty of Medicine and Pharmacy, Department of Mathematics and Informatics, Str. Universitatii no.1, 410087, Oradea, Str. Universitatii no.1, 410087, Oradea, Romania. Romania. firstname.lastname@example.org